Term
| When do we use an independent measures ANOVA? |
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Definition
| when there is more than 2 groups or levels of the IV |
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Term
| What's the difference between independent measures, repeated measures, and mixed ANOVA designs? |
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Definition
independent:
repeated:
mixed: more than 1 IV at the same time |
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Term
| What is generally learned from ANOVA? |
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Definition
| Tells whether means of samples that undergo different levels of the IV come from populations with the same or different means. |
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Term
| What are the hypotheses for ANOVAs? |
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Definition
H0: μ1 = μ2 = μ3 = …μk
H1: At least one μ is different from others. |
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Term
| Why do we need ANOVA when a series of t tests would test several hypotheses? |
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Definition
| The overall chance of type 1 error is the sum of all individual scores --> if you conduct 5 HT at alpha .05, the end chance of type 1 error is .25. It is also a lot more work. |
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Term
| What is the difference between test-wise and experiment-wise alpha level? |
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Definition
test-wise: level of error set for 1 test
experiment-wise: level of all tests combined on 1 set of data or study
*every test conducted increases 2nd type of alpha level |
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Term
| How does ANOVA help with the experiment-wise alpha level? |
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Definition
| makes all comparisons between means simultaneous and keeps alpha at level set by experimentor (even if compare many levels or groups) |
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Term
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Definition
is the variable manipulated
– Called a factor in ANOVA designs
– May have many factors in experiment |
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Term
| Quasi-Independent Variable |
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Definition
| not actively manipulated, but may affect experiment (ie gender, age, education, etc) |
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Term
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Definition
| Variable that designates the groups being compared |
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Term
| Between-Treatments Variance |
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Definition
| calculate the variance between treatment groups to provie a measure of the overall differences between treatment conditions --> really measures the differences between sample means |
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Term
| Within-Treatments Variance |
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Definition
| The variability within each sample --> provides a measure of the variability inside each treatment condition |
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Term
| Why is variance partitioned in ANOVA? |
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Definition
In this way ANOVA shows if differences between sample means are greater than
would be expected by chance. |
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Term
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Definition
| The MS value in the denominator of the F-ratio is called the error term. This MS value is intended to measure the amount of error variability - variability in the data for which there is no systematic or predictable explanation. It is used as a standard for determining whether or not the differences between treatments (measured by MSbtwn) are greater than would be expected just by chance. |
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Term
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Definition
| MSbetween - simply measure how much difference exists between the treatement means. The bigger the mean differences, the bigger the F-ratio. |
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Term
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Definition
| MSwithin - measures the variance of the scores inside each treatment; that is, the variance for each of the separate samples. In general, the larger the sample variances, the smaller is the F-ratio. |
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Term
| What contributes to the between groups source of variance in the independent measures ANOVA? |
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Definition
| MSbetween is composed of (SSbetween) / (dfbetween) |
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Term
| What contributes to teh within group source of variance in this test? |
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Definition
| MS within = (SSwithin) / (dfwithin) |
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Term
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Definition
| the number of individual treatment conditions; the number of levels of treatments |
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Term
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Definition
| the number of raw scores in each individual treatment condition |
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Term
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Definition
| total number of raw scores in the entire study; OR k times n, when n is constant |
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Term
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Definition
| sum of all scores in the entire study (sigma X) |
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Term
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Definition
| grand total, sum of all scores in the entire study (sigma T) |
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Term
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Definition
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Term
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Definition
- family of curves based on 2 separate dfs
- tells all values F could be and probability of getting each
- all F values are positive because they are variances
- positively skewed (always 1-tailed)
- median value is about 1; the more extreme the Fobt, the more likely you can reject Ho
- Fobt = 1.00 --> retain null |
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Term
| Why do we need 2 dfs to look up a critical F value? |
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Definition
df between (numerator) --> top
df within (denominator) --> down side |
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Term
| What assumptions are required for IM ANOVA? |
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Definition
- scores are drawn from normal distributions (large enough sample size)
- homogeneity of variance (errors are unrelated)
- observations are independent
- violations of assumptions dealt with in separate tests after F test is run
* the only way groups can differ is in their means |
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Term
| How is sample variance accounted for in ANOVA? |
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Definition
| – MSwithin works like s^2p |
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Term
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Definition
– When using 2 groups / treatmen conditions
– ANOVA may be used with 2 groups, under
certain conditions |
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Term
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Definition
- Percentage of variance accounted for
due to treatment
- Tells how much of variability
between scores explained by treatment effect
η = SSb / SSt |
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Term
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Definition
Determine which μ or μs actually
different from others
– Pairwise comparisons compare just 2 μs
–May be planned or unplanned
–Must keep experiment-wise alpha in
mind to avoid Type I error so don’t run too many…
- designed to reduce type 1 error |
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Term
| Give 2 examples of post hoc tests |
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Definition
1. Dunn test: divide alpha by number of planned comparisons
– Plan 2 post hoc comparisons
– 0.05/2 = 0.025 is new alpha for
each post hoc test
2. Tukey’s HSD: Single value determines minimum difference between treatments necessary for significance
- better for unplanned comparisons
HSD = q (sq.rt. MSw/n) |
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